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A subspace expanding technique for global zero finding of multi-degree-of-freedom nonlinear systems

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Applied Mathematics and Mechanics(English Edition) 2020年第5期41卷 769-784页

作者： Zigang LI Jun JIANG LingHONG J.Q.SUN Department of Mechanics School of ScienceXi’an University of Science and TechnologyXi’an 710054China State Key Laboratory for Strength and Vibration Xi’an Jiaotong UniversityXi’an 710049China Department of Mechanical Engineering School of EngineeringUniversity of CaliforniaMercedCA 95343U.S.A.

A subspace expanding technique(SET) is proposed to efficiently discover and find all zeros of nonlinear functions in multi-degree-of-freedom(MDOF) engineering systems by discretizing the space into smaller subdomains, which are called cells. The covering set of the cells is identified by parallel calculations with the root bracketing method. The covering set can be found first in a low-dimensional subspace, and then gradually extended to higher dimensional spaces with the introduction of more equations and variables into the calculations. The results show that the proposed SET is highlyefficient for finding zeros in high-dimensional spaces. The subdivision technique of the cell mapping method is further used to refine the covering set, and the obtained numerical results of zeros are accurate. Three examples are further carried out to verify the applicability of the proposed method, and very good results are achieved. It is believed that the proposed method will significantly enhance the ability to study the stability, bifurcation,and optimization problems in complex MDOF nonlinear dynamic systems.

关键词： spatial discretization subspace expanding technique(SET) parallel computing subdivision global zero finding

Aircraft Landing Gear Control with Multi-Objective Optimization Using Generalized Cell Mapping

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Transactions of Tianjin University 2015年第2期21卷 140-146页

作者：孙建桥贾腾熊夫睿秦志昌吴卫国丁千 School of Mechanical Engineering Tianjin University School of Engineering University of California

This paper presents a numerical algorithm tuning aircraft landing gear control system with three objectives,including reducing relative vibration, reducing hydraulic strut force and controlling energy consumption. Sliding mode control is applied to the vibration control of a simplified landing gear model with uncertainty. A two-stage generalized cell mapping algorithm is applied to search the Pareto set with gradient-free scheme. Drop test simulations over uneven runway show that the vibration and force interaction can be considerably reduced, and the Pareto optimum form a tight range in time domain.

关键词： landing gear sliding mode control model uncertainty multi-objective optimization generalized cellmapping

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非自治分数阶Duffing系统的激变现象

物理学报 2016年第18期65卷 226-233页

作者：刘晓君洪灵江俊西北农林科技大学理学院杨凌712100 西安交通大学机械结构强度与振动国家重点实验室西安710049

对一个非自治分数阶Duffing系统的激变现象进行了研究.首先介绍了一种研究分数阶非线性系统全局动力学的数值方法,即拓展的广义胞映射方法 (EGCM).该方法是基于分数阶导数的短记忆原理,并结合了广义胞映射方法和改进的预估校正算法,根... 详细信息

对一个非自治分数阶Duffing系统的激变现象进行了研究.首先介绍了一种研究分数阶非线性系统全局动力学的数值方法,即拓展的广义胞映射方法 (EGCM).该方法是基于分数阶导数的短记忆原理,并结合了广义胞映射方法和改进的预估校正算法,根据胞空间的特点,将胞尺寸作为截断误差的参考值,以此得到了一步映射时间的估算公式.用EGCM方法分别研究了分数阶Duffing系统随分数阶导数的阶数和外激励强度变化发生的边界激变和内部激变.并基于此,将激变拓展定义为混沌基本集与周期基本集之间的碰撞,其中混沌基本集包括混沌吸引子,边界上的混沌集合以及吸引域内部的非混沌吸引子的混沌集合.所得结果进一步说明了EGCM方法对于分析分数阶系统全局动力学的有效性.

关键词：关键词分数阶系统混沌激变

流体惯性对弹性环式挤压油膜阻尼器-转子系统动力特性的影响

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航空动力学报 2018年第12期33卷 2981-2990页

作者：王晓娟韩知非丁千张微天津大学机械工程学院天津300350

基于考虑流体惯性的雷诺方程,利用有限差分法计算弹性环式挤压油膜阻尼器(ERSFD)的内、外油膜分布压力和油膜合力,分析ERSFD-转子系统动力学。通过比较考虑流体惯性和不考虑流体惯性时的油膜压力、油膜合力和转子幅频响应,发现当雷诺数... 详细信息

基于考虑流体惯性的雷诺方程,利用有限差分法计算弹性环式挤压油膜阻尼器(ERSFD)的内、外油膜分布压力和油膜合力,分析ERSFD-转子系统动力学。通过比较考虑流体惯性和不考虑流体惯性时的油膜压力、油膜合力和转子幅频响应,发现当雷诺数较大时,计算结果存在明显差异。考虑流体惯性的转子系统等效刚度和阻尼均更大,临界转速更大,而共振区振幅则更小。当转子系统的转速较大,或油膜黏度较小从而雷诺数较大时,在油膜力计算中考虑流体惯性的影响是必要的。

关键词：弹性环式挤压油膜阻尼器流体惯性转子系统雷诺数油膜力

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接触刚度对制动摩擦块时域-频域响应的影响

振动与冲击 2019年第8期38卷 198-202页

作者：隋鑫丁千天津大学机械工程学院天津300350 天津市非线性动力学与控制重点实验室天津300350

考虑Stribeck效应的摩擦力,建立摩擦块-制动盘耦合动力学方程。应用Runge-Kutta法和有限差分法数值模拟相对移动作用下的系统振动。主要分析摩擦块切向运动的动力学特性,揭示表面接触刚度比对其Hopf分岔的影响,并应用时域-频域分析方法... 详细信息

考虑Stribeck效应的摩擦力,建立摩擦块-制动盘耦合动力学方程。应用Runge-Kutta法和有限差分法数值模拟相对移动作用下的系统振动。主要分析摩擦块切向运动的动力学特性,揭示表面接触刚度比对其Hopf分岔的影响,并应用时域-频域分析方法得出摩擦块动力学特性随制动盘转动速度变化的规律,分析其黏滑振动机理。

关键词：盘式制动器移动载荷 Hopf分岔黏滑振动

基于自适应动态规划的主动质量阻尼系统振动控制

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应用力学学报 2021年第2期38卷 545-551页

作者：李智贾苏孙建桥丁千天津大学机械工程学院天津300350 加州大学工程学院默塞德95343

主动质量阻尼(AMD)系统是一种主动减振控制技术,其核心在于控制策略的设计。针对该系统力学模型中参数不确定性和外部载荷随机性问题,本文采用数据驱动的自适应动态规划(ADP)算法,设计基于ADP的鲁棒控制器。构建评价神经网络和执行神经... 详细信息

主动质量阻尼(AMD)系统是一种主动减振控制技术,其核心在于控制策略的设计。针对该系统力学模型中参数不确定性和外部载荷随机性问题,本文采用数据驱动的自适应动态规划(ADP)算法,设计基于ADP的鲁棒控制器。构建评价神经网络和执行神经网络,分别逼近代价函数和控制策略,在系统模型参数完全未知的情况下,通过采集系统振动响应数据进行双神经网络权值迭代,可以得到近似最优控制策略。通过在一个受基础激励的模拟结构系统上安装AMD系统进行仿真分析,结果表明,基于数据驱动的ADP算法,对模型参数未知的受控结构具有良好的振动控制效果。

关键词：振动控制数据驱动自适应动态规划主动质量阻尼系统

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

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Applied Mathematics and Mechanics(English Edition) 2019年第12期40卷 1759-1776页

作者： Lincong CHEN Haisheng ZHU J.Q.SUN College of Civil Engineering Huaqiao UniversityXiamen 361021Fujian ProvinceChina School of Engineering University of CaliforniaMercedCA 95343U.S.A

The vibroimpact systems with bilateral barriers are often encountered in ***,the dynamics of the vibroimpact system with bilateral barriers is full of *** closed-form solutions were *** this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous *** probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)*** closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability ***,the versatility of the proposed approach is demonstrated by its application to two typical *** that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

关键词： bilateral barrier vibroimpact system weighted residue method iterative random vibration

A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems

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Applied Mathematics and Mechanics(English Edition) 2020年第6期41卷 967-982页

作者： Lincong CHEN J.Q.SUN College of Civil Engineering Huaqiao UniversityXiamen 361021Fujian ProvinceChina Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province Jimei Avenue 668Xiamen 361021Fujian ProvinceChina Department of Mechanical Engineering School of EngineeringUniversity of CaliforniaMercedCA 95343U.S.A.

Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical *** paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.

关键词： stationary response multi-degree-of-freedom(MDOF)nonlinear system Fokker-Planck-Kolmogorov(FPK)equation least square method

Influence of Design Reference on Tracking Performance of Feedback Control

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Transactions of Tianjin University 2018年第1期24卷 66-72页

作者： Qiqi Zhao Zhichang Qin Jianqiao Sun School of Mechanical Engineering Tianjin University School of Engineering University of California Merced

In this paper, we present an investigation on the tracking performances of feedback control as a function of reference signals. We use multi-objective optimal designs of feedback controls as a fair basis for comparing different control designs, and examine step, ramp, and periodic signals at various frequencies. Through comparing the tracking performances of controls designed with different reference signals,we find that the controls designed with ramp signals perform better in tracking step and ramp references than those designed with step signals. To track periodic signals, we find that the controls designed with periodic signals at the same frequency generally provide the best performance, and those designed with step and ramp signals perform comparably.

关键词： Reference signal Tracking performance Feedback control Multi-objective optimization